Modern Physics Ques 168
- The wavelength of $K _{\alpha}, X$-rays produced by an X-ray tube is $0.76 $ $\AA$. The atomic number of the anode material of the tube is ……..
(1996, 2M)
Show Answer
Answer:
Correct Answer: 168.$(39)$
Solution:
Formula:
Wavelength Corresponding To Spectral Lines:
- $\frac{1}{\lambda _{K _{\alpha}}}=R(Z-1)^{2} (\frac{1}{1^{2}}-\frac{1}{2^{2}})=\frac{3}{4} R(Z-1)^{2}$
$ \therefore \quad(Z-1)=\frac{2}{\sqrt{3 R \lambda _{K _{\alpha}}}} $
Here, $R=$ Rydberg’s constant
$ =1.097 \times 10^{7} m^{-1} \text { and } $
$ \lambda _{K _{\alpha}}=0.76 \AA=0.76 \times 10^{-10} m $
Substituting the values, we have
$ \text { or } \quad Z=39 $
BETA
